McCleary--Rubin reconstruction for simple forest-skein groups

Abstract

A simple Ore forest-skein category produces three infinite groups analogous to Richard Thompson's groups F,T,V. We prove that reconstruction theorems of McCleary and Rubin apply to them: each of these groups encodes a canonical action by homeomorphisms. This provides powerful invariants that we use to distinguish infinitely many explicit simple groups that are finitely presented (of type $F_\infty$).